Detecting the entanglement structure, such as intactness and depth, of an n-qubit state is important for understanding the imperfectness of the state preparation in experiments. However, identifying such structure usually requires an exponential number of local measurements. In this letter, we propose an efficient machine learning based approach for predicting the entanglement intactness and depth simultaneously. The generalization ability of this classifier has been convincingly proved, as it can precisely distinguish the whole range of pure generalized Greenberger–Horne–Zeilinger (GHZ) states which never exist in the training process. In particular, the learned classifier can discover the entanglement intactness and depth bounds for the noised GHZ state, for which the exact bounds are only partially known.

检测n- qubit 状态的纠缠结构，例如完整性和深度，对于理解实验中状态准备的不完善性非常重要。然而，识别这种结构通常需要指数数量的局部测量。在这封信中，我们提出了一种有效的基于机器学习的方法，用于同时预测纠缠完整性和深度。该分类器的泛化能力已得到令人信服的证明，因为它可以精确区分训练过程中从未存在的纯广义 Greenberger-Horne-Zeilinger (GHZ) 状态的整个范围。特别是，学习的分类器可以发现噪声 GHZ 状态的纠缠完整性和深度边界，其确切边界仅部分已知。